1 . 已知数列
的通项公式
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f448cebfaf66b70a4c8485bde0398d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb23c6a9e8a42faef0a84be8ad6b008.png)
A.99 | B.100 | C.101 | D.102 |
您最近一年使用:0次
解题方法
2 . 已知等比数列
的公比
,前
项和为
,且
,
.数列
满足
.
(1)求数列
、
的通项公式;
(2)求数列
的前
项的和;
(3)记
为区间
内整数的个数
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28171b364c85b51806eddb2c210cc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e85d3bc21a3f9e2a81cd7a359df619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bde034b0bb6767f923526db8a387c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d8308f4d32da07e0b4e161658f0cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe2e15ba11f38188ba4445117d0914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4159b10615a3bafbf9f36e6f19fc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc1e7a87da7751da31f851ae6d46aff.png)
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2020-09-23更新
|
1032次组卷
|
3卷引用:湖北省新高考联考协作体2020-2021学年高二上学期开学联考数学试题
湖北省新高考联考协作体2020-2021学年高二上学期开学联考数学试题苏教版(2019) 选修第一册 选填专练 第4章 微专题十一 数列中常见求和问题(已下线)专题11 数列前n项和的求法 微点3 裂项相消法求和(一)
名校
解题方法
3 .
为数列
的前
项和满足:
.
(1)设
,证明
是等比数列;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68c466e8bc7621b3523c49a30d1bd55.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e680f28daa101a42903ef44cf6e6894a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2020-05-23更新
|
629次组卷
|
4卷引用:河北省石家庄市第二中学2019-2020学年高三下学期教学质量检测(开学考试)数学(理)试题
4 . 已知有穷数列A:
(
且
).定义数列A的“伴生数列”B:
,其中
(
),规定
,
.
(1)写出下列数列的“伴生数列”:
①1,2,3,4,5;
②1,
,1,
,1.
(2)已知数列B的“伴生数列”C:
,
,…,
,…,
,且满足
(
,2,…,n).
(i)若数列B中存在相邻两项为1,求证:数列B中的每一项均为1;
(ⅱ)求数列C所有项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55aea2d6309205fe59687ea3440bb2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfe398651d365506cabd498ee5d1556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860a70d427b4c46206e43f17299e9b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11829c0cd3e74ffdf951e2d484718d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b740bc48c9718a294c11a1485fd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897b606fdc64a88a0938d3d60c3ea3e9.png)
(1)写出下列数列的“伴生数列”:
①1,2,3,4,5;
②1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(2)已知数列B的“伴生数列”C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d84a2027dc4157991c40673b6b4d23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
(i)若数列B中存在相邻两项为1,求证:数列B中的每一项均为1;
(ⅱ)求数列C所有项的和.
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2020-05-12更新
|
743次组卷
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2卷引用:北京市第五中学2023届高三上学期第一次阶段检测数学试题
名校
5 . 已知
为数列
的前
项和,
,
,平面内三个不共线的向量
,
,
满足
,若点
,
,
在同一直线上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b30c3d7cc1e41af67e909df3f39830.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911c0a2ab5e2e85f1ad267f41cb96b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794efd8cf0cc386faa170d01f357b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7195a0b5b59c9462b9faaf5a9fcfc6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b855acafb6c888420224f6f052f416c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b30c3d7cc1e41af67e909df3f39830.png)
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2019-11-14更新
|
408次组卷
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2卷引用:上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题
名校
6 . 若定义在R上的函数
满足:对于任意实数x、y,总有
恒成立,我们称
为“类余弦型”函数.
已知
为“类余弦型”函数,且
,求
和
的值;
在
的条件下,定义数列
2,3,
求
的值.
若
为“类余弦型”函数,且对于任意非零实数t,总有
,证明:函数
为偶函数,设有理数
,
满足
,判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0552c4870a3d5da4531c66c9e0998c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9535576eccc7f217fadcfe547efe35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a77c4d65f01e583b2f6c5ea97c3e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687421a4825fb98630a0647520129942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68b86d6227320642dc65e23837668bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63dfad2cc3e89a54167be3a1b65c67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2c8508a530cc066c2a93838e3bf07f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91882eb813ad04a08dc0b58a4b50a5da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa33c2bd791339d32821077846605d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78c60f95efd63c0183315324d10ee29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed46533654ddbd25e8eaba7c3ada0533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e27e84da7c25bef88187f2ffaea3bfc.png)
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2020-01-01更新
|
894次组卷
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3卷引用:上海市七宝中学2018-2019学年高三上学期摸底考试数学试题
名校
7 . 数列
的通项公式
,其前
项和为
,则
等于_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06dd07bcdcf34c4cbeb9a07462407e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e398c6f4b0f5247906161e084ed2d.png)
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2019-07-01更新
|
799次组卷
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2卷引用:浙江省金华市曙光学校2019-2020学年高一下学期返校测试数学试题
8 . 设数列
是首项为0的递增数列,函数
满足:对于任意的实数
,
总有两个不同的根,则
的通项公式是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7535ab1819efecd58e89dbf65e1aa0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c91d6d2c9deb4722c6a7b21358b213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa2524fcaedaeb1a8b55df6d8c9bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2019-11-13更新
|
1235次组卷
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20卷引用:2017届河南郑州一中网校高三入学测试数学(理)试卷
2017届河南郑州一中网校高三入学测试数学(理)试卷2016-2017学年湖北宜昌葛洲坝中学高二理上期中数学试卷12016-2017学年湖北宜昌葛洲坝中学高二理上期中数学试卷2河北省武邑中学2017届高三下学期一模考试数学(文)试题【全国百强校】福建省厦门外国语学校2019届高三11月月考数学(理)试题上海市金山中学2016-2017学年高一下学期期末数学试题上海市南洋模范中学2018-2019学年高三上学期第一次月考数学试题2018届上海市大同中学高三上学期期中数学试题上海市七校(北虹,上理工附中,同二,光明,六十,卢高,东昌)2016届高三下学期3月联考(理)数学试题2016届上海市七校联考高考一模(理科)数学试题上海市理工附中等七校2016届高三下学期3月联考(文)数学试题上海市七校2016届高三下学期3月联考(文)数学试题福建省泰宁第一中学2020届高三上学期第二次阶段考试数学(理)试题(已下线)第7章 三角函数(能力提升)-2020-2021学年高一数学下册单元测试定心卷(沪教版2020必修第二册)(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)上海期末真题精选50题(小题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)专题4-1 三角函数性质、最值和w小题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)上海市建平中学2021届高三冲刺模拟卷3数学试题(已下线)专题06 三角函数(模拟练)-1上海市西南位育中学2021-2022学年高二下学期期末数学试题
12-13高一下·四川成都·阶段练习
名校
9 . 已知数列
的通项公式为
,设其前n项和为
,则使
成立的自然数n
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4acfae9db9e2f0e7904e0614c53a553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572ad94be91581e4ab3c92ef4be8cadb.png)
A.有最小值63 | B.有最大值63 |
C.有最小值31 | D.有最大值31 |
您最近一年使用:0次
2020-02-28更新
|
373次组卷
|
7卷引用:2016届辽宁省五校协作体高三上学期期初考试文科数学试卷
名校
10 . 对于数列
,定义
为
的“优值”,现已知某数列的“优值”
,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1226620ac12f4e28ee5461c95a83538c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4caa2574d37de2def69f51e81b0f553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466a22f3320bb2340bab262cab2d713e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1226620ac12f4e28ee5461c95a83538c.png)
A.2022 | B.1011 | C.2020 | D.1010 |
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2018-12-17更新
|
2547次组卷
|
8卷引用:黑龙江省哈尔滨师范大学青冈实验中学校2019-2020学年高二上学期开学考试(8月)数学试题
黑龙江省哈尔滨师范大学青冈实验中学校2019-2020学年高二上学期开学考试(8月)数学试题湖南省岳阳市汨罗市二中2020-2021学年高三上学期入学考试数学试题【全国百强校】湖南师范大学附属中学2019届高三上学期月考(四)数学(理)试题湖南省邵东县创新实验学校2019届高三第五次月考数学(理)试题2020届湖南省长沙市长郡中学高三上学期月考(四)数学(文)试题2019届湖南师大附中高三月考试卷(四)数学(理科)试题四川省宜宾市叙州区第二中学2020-2021学年高三上学期阶段二考试数学(文)试题(已下线)第4章 数列(基础卷)-2021-2022学年高二数学新教材单元双测卷(苏教版2019选择性必修第一册)